Not Applicable
Not Applicable
The present invention relates to devices for controlling mass flow, and more particularly, to methods and devices for conditioning the flow to improve the sensitivity and accuracy of such a device.
Consider the system 10 shown in block diagram form in FIG. 1, which includes an inlet reservoir 12 coupled to a measurement chamber 14. The inlet reservoir 12 is characterized by an inlet pressure Pi(t). The measurement chamber 14 is characterized by an inlet port 16 where the inlet reservoir 12 is coupled to the measurement chamber 14, an internal volume V, and an internal pressure P(t). An inlet flow Q(t) flows from the inlet reservoir 12 to the measurement chamber 14 through the inlet port 16. The rate of change of the pressure P(t) within the measurement chamber 14 as a function of time may be given by:                                           ⅆ                          P              ⁡                              (                t                )                                                          ⅆ            t                          =                                            P              .                        ⁡                          (              t              )                                =                                                    P                STP                            V                        ⁢                          Q              ⁡                              (                t                )                                                                        (        1        )            
where PSTP is the chamber pressure at standard temperature and pressure. Equation (1) may be rewritten to solve for the inlet flow, i.e.,                               Q          ⁡                      (            t            )                          =                                                            P                .                            ⁡                              (                t                )                                      ⁢            V                                P            STP                                              (        2        )            
Thus, the inlet flow may be calculated as a function of the time rate of change of the chamber pressure {dot over (P)}(t) and the volume of the chamber V. The volume of the chamber V may be easily measured, and the time rate of change of the chamber pressure {dot over (P)}(t) may be acquired by employing a pressure sensor 18 combined with a digital differentiation scheme 20 (see, for example, S. K. Mitra and J. F. Kaiser, xe2x80x9cHandbook for Digital Signal Processing,xe2x80x9d John Wilcy and Sons, 1993, Chapter 13). However, a practical digital differentiator 20 samples the pressure data at a maximum sampling frequency, filters the sampled data, and performs the time derivative of the sampled, filtered data. Such a digital differentiator 20 only produces accurate results for pressure variations having frequencies less than a fraction of the maximum sampling frequency, as shown in the graph of FIG. 2. This graph plots the normalized differentiator output against the normalized frequency of the pressure variation (normalized to the sampling frequency) for an ideal differentiator 30 and the practical differentiator 32 discussed above. The practical digital differentiator 32 tracks the ideal differentiator 30 for frequencies up to approximately 0.4 of the sampling frequency, and radically departs from the ideal for higher frequencies of pressure variations. Thus, rapid pressure changes that are greater than 40 percent of the sampling frequency cannot be accurately measured by the configuration of FIG. 1. This point of departure from the ideal differentiator is referred to herein as the xe2x80x9cdifferentiator cutoff frequency.xe2x80x9d
It is an object of the present invention to substantially overcome the above-identified disadvantages and drawbacks of the prior art.
The foregoing and other objects are achieved by the invention which in one aspect comprises an apparatus for conditioning a gas flow to improve a measurement of rate of pressure change associated with the gas flow. The apparatus includes a measurement chamber having an interior portion characterized by an internal volume, and an inlet port for receiving the gas flow. The apparatus also includes a pressure sensor for sensing a pressure within the interior portion of measurement chamber and for producing a pressure signal corresponding the pressure within the measurement chamber. The apparatus also includes a signal processor for receiving, sampling the pressure signal at a sampling frequency and filtering the pressure signal so as to produce a sampled pressure signal. The signal processor further calculates a time derivative of the sampled pressure signal. The apparatus also includes an inlet damper disposed at the inlet port, constructed and arranged such that the gas flow passes, at least partially, through the inlet damper prior to passing through the inlet port and into the measurement chamber. The inlet damper modifies one or more characteristics of the gas flow as a function of a pressure drop across the inlet damper, according to a damper transfer function. The internal volume and the damper transfer function are selected so as to the frequencies associated with variations of the pressure in the measurement chamber to a predetermined fraction of the sampling frequency.
In another embodiment, the pressure sensor is disposed within the interior portion of the measurement chamber.
In another embodiment, the pressure sensor is disposed at the inlet port, and produces a pressure signal corresponding to an inlet flow pressure.
In another embodiment, the damper transfer function describes a linear relationship between (i) the pressure drop across the inlet damper and (ii) the gas flow through the inlet damper.
In another embodiment, the damper transfer function describes a non-linear relationship between (i) the pressure drop across the inlet damper and (ii) the gas flow through the inlet damper.
In another embodiment, the predetermined fraction of the sampling frequency corresponds to a performance limit associated with the signal processor for calculating a time derivative of the sampled pressure signal
In another embodiment, the predetermined fraction of the sampling frequency is about 0.4.
In another embodiment, the apparatus further includes a flow sensor for measuring the gas flow through the inlet port and for producing a flow signal corresponding to the gas flow through the inlet port. The apparatus also includes an outlet port on the measurement chamber for passing an outlet gas flow, and a valve disposed at the outlet port for controlling the outlet gas flow. The signal processor (i) combines the flow signal with the time derivative of the sampled pressure signal so as to produce an estimate of the outlet gas flow, and (ii) controls the valve as a function of the estimate, so as to produce a substantially constant outlet gas flow.
In another embodiment, the damper is disposed before the flow sensor.
In another embodiment, the damper is disposed after the flow sensor, and before the pressure sensor.
In another aspect, the invention comprises a method of conditioning a gas flow to improve a measurement of rate of pressure change associated with the gas flow. The method includes providing a measurement chamber having an interior portion characterized by an internal volume, and an inlet port for receiving the gas flow. The method also includes sensing a pressure within the interior portion of measurement chamber and producing a pressure signal corresponding the pressure within the measurement chamber. The method further includes sampling the pressure signal at a sampling frequency and filtering the pressure signal so as to produce a sampled pressure signal, and calculating a time derivative of the sampled pressure signal. The method further includes damping the gas flow through the inlet port via an inlet damper disposed at the inlet port, so as to modify one or more characteristics of the gas flow as a function of a pressure drop across the inlet damper, according to a damper transfer function. The method also includes selecting the internal volume and the damper transfer function so as to limit a frequency associated with variations of the pressure within the measurement chamber to a predetermined fraction of the sampling frequency.
Another embodiment further includes disposing the pressure sensor within the interior portion of the measurement chamber.
Another embodiment further includes disposing the pressure sensor at the inlet port, such that the pressure sensor produces a pressure signal corresponding to an inlet flow pressure.
Another embodiment further includes providing a damper transfer function that describes a linear relationship between (i) the pressure drop across the inlet damper and (ii) the gas flow through the inlet damper.
Another embodiment further includes providing a damper transfer function that describes a non-linear relationship between (i) the pressure drop across the inlet damper and (ii) the gas flow through the inlet damper.
Another embodiment further includes selecting the internal volume and the damper transfer function so as to limit a frequency associated with variations of the pressure within the measurement chamber to a predetermined fraction of the sampling frequency corresponding to a performance limit associated with the signal processor for calculating a time derivative of the sampled pressure signal.
Another embodiment further includes selecting the internal volume and the damper transfer function so as to limit a frequency associated with variations of the pressure within the measurement chamber to a predetermined fraction of the sampling frequency of about 0.4 of the sampling frequency.
Another embodiment further includes measuring the gas flow through the inlet port and producing a flow signal corresponding to the gas flow through the inlet port. This embodiment also includes providing an outlet port on the measurement chamber for passing an outlet gas flow, and combining the flow signal with the time derivative of the sampled pressure signal so as to produce an estimate of the outlet gas flow. This embodiment also includes controlling the outlet gas flow at the outlet port as a function of the estimate, so as to produce a substantially constant outlet gas flow.
Another embodiment further includes disposing the damper before the flow sensor.
Another embodiment further includes disposing the damper after the flow sensor, and before the pressure sensor.